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5. What is the next number in this pattern? \[ 0.54,0.6,0.66,0.72, \ldots, \ldots \]

Ask by Stewart Dunn. in the United States
Mar 11,2025

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Answer

The next number in the pattern is 0.78.

Solution

To find the next number in the pattern \(0.54, 0.6, 0.66, 0.72, \ldots\), let's first analyze the differences between the consecutive numbers: 1. The difference between \(0.6\) and \(0.54\) is: \[ 0.6 - 0.54 = 0.06 \] 2. The difference between \(0.66\) and \(0.6\) is: \[ 0.66 - 0.6 = 0.06 \] 3. The difference between \(0.72\) and \(0.66\) is: \[ 0.72 - 0.66 = 0.06 \] From this, we can see that the pattern increases by \(0.06\) each time. To find the next number after \(0.72\), we add \(0.06\) to it: \[ 0.72 + 0.06 = 0.78 \] Thus, the next number in the pattern is \(0.78\).

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The pattern in the sequence involves repeatedly adding 0.06 to each number to obtain the next number. After 0.54, we have 0.6 (which is 0.54 + 0.06), then 0.66 (0.6 + 0.06), followed by 0.72 (0.66 + 0.06). Continuing this pattern, we add 0.06 to 0.72, resulting in 0.78. Therefore, the next number in the pattern is 0.78. So the sequence continues with: 0.54, 0.6, 0.66, 0.72, **0.78**.

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